   Chapter 16.1, Problem 6E

Chapter
Section
Textbook Problem

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9.6. F ( x , y ) = y   i   −   x   j x 2 + y 2

To determine

To sketch: The vector field F(x,y)=yixjx2+y2 .

Explanation

Given data:

F(x,y)=yixjx2+y2

Formula used:

Consider a two-dimensional vector F=x,y .

Write the expression for length of the two dimensional vector.

|F(x,y)|=x2+y2 (1)

F(x,y)=yixjx2+y2 (2)

F(x,y)=yx2+y2ixx2+y2j=yx2+y2,xx2+y2

Find the length of F(x,y) using equation (1).

|F(x,y)|=(yx2+y2)2+(xx2+y2)2=(y2x2+y2)+(x2x2+y2)=y2+x2x2+y2=1

Simplify |F(x,y)| as follows

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